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2 Answers
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～たところ and ～たばかり both mean "just did X". I was always taught that ～たところ means "I just did X and haven't done anything else, whereas ～たばかり means "I just did X (but could've been a little while ago)." The "scope" of the event can determine the recentness.

例

昼食を食べたところだ。 → I just ate lunch (right now).

（午後３：００) 昼食食べたばかりなんで、眠たい。 → (At 3:00pm) I just ate lunch (even though it was several hours ago), so now I'm sleepy.

(隣の人に車を見せながら） 新しい車買ったところやで！ → (Show his neighbor) I just bought this new car (as in just came home from the dealership)!

（電車の改札口で） 森内さん、回数券多いね。新しい車買ったばかりじゃない？ → (At the ticket gate for the train) Moriuchi, you sure do have a lot of commuter (train) tickets. Didn't you just buy a new car? (could have been several days or even a few weeks ago).